In this page integration worksheet2 solution1 we are going to see
solution of some practice question from the worksheet of integration.

**Question 1**

(i) Integrate the following with respect to x , x⁴

**Solution:**

The given question exactly matches the formula

**∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c**

Now we are going to integrate the given question by using this formula in the question instead of n we have 4

So we get,

∫ x⁴ dx = x^(4 + 1)/(4 + 1)

= (x^5/5) + C

(ii) Integrate the following with respect to x , (x + 3) ⁵

**Solution:**

The given question exactly matches the formula

**∫ (ax + b)ⁿ dx = (1/a) [(ax + b)^⁽ⁿ ⁺ ¹⁾/(n + 1)] + c**

Now we are going to integrate the given question by using this formula in the question instead of n we have 5

So we get,

∫ (x + 3)⁵ dx = (x + 3)^(5 + 1)/(5 + 1)

= (x + 3)^6/6 + C

= (1/6)(x + 3)^6 + C

(iii) Integrate the following with respect to x , (3 x + 4) ⁶

**Solution:**

The given question exactly matches the formula

**∫ (ax + b)ⁿ dx = (1/a) [(ax + b)^⁽ⁿ ⁺ ¹⁾/(n + 1)] + c**

Now we are going to integrate the given question by using this formula in the question instead of "n" we have 6 and instead of "a" we have 3

So we get,

∫ (3 x + 4) ⁶ dx = (3 x + 4)^(6 + 1)/(6 + 1)

= (1/3)[(3 x + 4)^7/7] + C

= (1/21)(3 x + 4)^7 + C

(iv) Integrate the following with respect to x , (4 - 3 x) ⁷

**Solution:**

The given question exactly matches the formula

**∫ (ax + b)ⁿ dx = (1/a) [(ax + b)^⁽ⁿ ⁺ ¹⁾/(n + 1)] + c**

Now
we are going to integrate the given question by using this formula in
the question instead of "n" we have 7 and instead of "a" we have -3

So we get,

∫ (4 - 3 x) ⁷ dx = (4 - 3 x)^(7 + 1)/(7 + 1)

= (-1/3)[(4 - 3 x)^8/8] + C

= (-1/24)(4 - 3 x)^8 + C

(v) Integrate the following with respect to x , (L x + m) ⁸

**Solution:**

The given question exactly matches the formula

**∫ (ax + b)ⁿ dx = (1/a) [(ax + b)^⁽ⁿ ⁺ ¹⁾/(n + 1)] + c**

Now
we are going to integrate the given question by using this formula in
the question instead of "n" we have 8 and instead of "a" we have L

So we get,

∫ (L x + m)⁸ dx = (L x + m)^(8 + 1)/(8 + 1)

= (1/L)[(L x + m)^9/9] + C

= (1/9 L)(L x + m)^8 + C

integration worksheet2 solution1 integration worksheet2 solution1

- Back to worksheet
- Integration
- Substitution method
- Decomposition method
- Properties of integrals
- Integration-by parts
- Integration-of Sec³ x
- Standard integrals
- Integrating quadratic denominator
- Integration-using partial fractions
- Definite integrals